Theorem 2.16 (Equivalence of classes in the range \(0\le \delta <\rho \le 1,\)  \(\rho \ge 1-\delta ,\)  [1]}, [2]})  Let \(A:C^{\infty }(G)\rightarrow {D}^{\prime }(G)\)  be a continuous linear operator and let \(0\le \delta <\rho \le 1,\)  with \(\rho \ge 1-\delta .\)  Then, \(A\in \Psi ^m_{\rho ,\delta }(G)\)  if and only if \(A\in \Psi ^m_{\rho ,\delta }(G\times \widehat{G}).\)

